প্ল্যান

বর্গমূল ও করণী সরলীকরণ ক্যালকুলেটর

65-এর বর্গমূল কত? √65 ≈ 8.062258, এবং এটি সরল হয় না কারণ 65-এর কোনো বর্গ উৎপাদক নেই। এই ক্যালকুলেটর যেকোনো মূল নির্ণয় করে এবং সরলতম করণী রূপে লেখে, যেমন √180 = 6√5।

পূর্ণসংখ্যা, দশমিক বা 2/3-এর মতো ভগ্নাংশ

ফলাফল

মান দিন এবং ফলাফল দেখতে “হিসাব করুন” চাপুন।

সূত্র

a2b=ab\sqrt{a^2 b} = a\sqrt{b}

Take square factors out of the root: √72 = √(36 × 2) = 6√2.

anbn=abn\sqrt[n]{a^n b} = a\sqrt[n]{b}

For an nth root, take out factors that are perfect nth powers.

এই ক্যালকুলেটর কীভাবে ব্যবহার করবেন

  1. Enter the number and choose which root you want.
  2. Press Calculate to get the simplified exact root and its decimal value.

সমাধান করা উদাহরণ

The square root of 72

72 = 36 × 2, and 36 = 6² is a perfect square.

√72 = √(6² × 2) = 6√2 ≈ 8.485281.

The square root of 65

65 = 5 × 13. Neither factor is a perfect square, so √65 is already in simplest radical form.

√65 lies between √64 = 8 and √81 = 9, very close to 8: √65 ≈ 8.062258.

Simplify a cube root: ∛54

Choose the cube root. 54 = 27 × 2, and 27 = 3³ is a perfect cube.

∛54 = ∛27 × ∛2 = 3∛2 ≈ 3.779763.

সাধারণ ভুল

  • Not using the largest square factor: √180 = 2√45 is true but unfinished — 45 still contains 9. The simplest form is 6√5.
  • Splitting a sum: √(9 + 16) is 5, not √9 + √16 = 7.
  • Treating the decimal as exact: √65 ≈ 8.062258 is rounded; √65 is the exact value.

প্রায়ই জিজ্ঞাসিত প্রশ্ন

How do you simplify √180?

180 = 36 × 5, so √180 = 6√5 ≈ 13.416408 in simplest radical form.

What is the square root of 2116?

46, because 46 × 46 = 2116. It is a perfect square, so the root is a whole number.

What is the square root of x⁶?

√(x⁶) = |x³|, because (x³)² = x⁶. For x ≥ 0 that is simply x³. This calculator works with numbers; the algebra calculator handles expressions with letters.

Why is the answer written as 6√2 instead of a decimal?

√2 never ends or repeats, so 6√2 is the exact answer. The decimal shown with it is rounded.

Can I take the root of a negative number?

Odd roots, yes: ∛(−27) = −3. Even roots (square, 4th, …) of a negative number are not real numbers.

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